2D Face Animation on 3D Model: Transparent Texture?
Your problem is that the UVs for the face got moved away from the skin material. Further, the skin material is separate from the eye material, which is ok if you are following the tutorial, but note that he superimposes the eye material onto the skin material with the Mix Shader node. You only have 1 UV map--this makes it so the eyes will never be in the right place; they will always be floating out in space, away from the skin texture. We can fix that.I will record a gif or something, hang on...

...do you have a version of the file with the eye region still attached to the mesh? We should start from there. Please upload that file. Use https://blend-exchange.giantcowfilms.com/





Oh! I can just attach the animation :j















...animating the new UV map "_EyesUV" will not have any effect on the body texture now. Here is the .blend file:



NOTE: if you are no longer satisfied with your textures, there are a couple of solutions:


Export your UV layout for the eyes in the UV editor (I suspect you already know how to do this) and warp the eye textures you already have into proper orientation in Photoshop.
paint directly onto the model in Blender (see any quick-and-dirty Youtube tutorial for that). I find this technique expecially useful for high-contrast texture features I know will look warped if I try to eyeball it in Photoshop.


ALSO, IMPORTANT: Texture will be warped until you de-parent armature. I do not know yet why the armature was an issue.

I deparented the armature, recalculated the bone rolls, reset the pose, and re-parented, and it works now:

Baking the Eyes object silhouette onto an image using the Body's Ambient Occlusion.




The "Collections" panel replaces the "Outliner" panel in Blender 2.8. You can find these same options there:


If the bake takes longer than you (I) thought, it's because the second UV map also has coordinates for the rest of the body (not sure how to remove those for the bake, maybe just drag them outside the UV canvas?). Save this image:


File: